Unified Field Theory of Matter + Light Without Quantum

The unfinished revolution of modern physics as quantum physics is unification with classical continuum physics expressed as Newton-Maxwell differential equations in terms of gravitational and electromagnetic fields as functions of 3d space coordinates and a time coordinate as real numbers forming a space-time continuum without smallest scale. 

Classical physics describes a macroscopic world of matter separated from a microscopic world of light as a Newton-Maxwell deterministic Field Theory covering a change of scale of $10^{35}$ from gravitation on billions of light-years down to nanometers of visible light. 

This seemed to be the end of physics, but with the start of the 20th century of modernity a discovered new world of atoms required something new beyond Newton-Maxwell. In 1925 Danish physicist Niels Bohr presented a model of the electron of the Hydrogen atom with energies restricted to the observed discrete spectrum of Hydrogen as a form quantisation, however without convincing physics.    

In 1926 Austrian physicist Erwin Schrödinger presented a model of the Hydrogen atom as an eigenvalue problem of classical form with the eigenvalues representing energies exactly corresponding to the observed spectrum of Hydrogen. This saved classical Field Theory in the case of only one electron, but the world of atoms with more than one electron remained to be modeled to maintain credibility of the new atomic physics.  

This is where history of physics took a turn which became the leading principle of modern physics through the 20th century into our time as a break with classical deterministic physics in 3 space dimensions into a new form of probabilistic physics in $3N$ space dimensions for an atom with $N>1$ electrons without clear physicality. This became the story of Standard Quantum Mechanics StdQM as the fundamental theory of modern physics. It came with the stroke of a pen by a purely formal extension by adding a new set of space variables for each new electron. An easy catch which however came with severe side effects of leaving classical deterministic continuum physics in 3d for a new world of probabilities instead of actualities. 

StdQM thus split physics into classical Newton-Maxwell continuum theory for macroscopic matter and microscopic light into new physics with main objective to describe the interaction between microscopic atoms and light. Physicists claimed to be forced to take this step by a Nature refusing to be described within classical continuum physics, in a heroic or rather desperate act of giving up classical ideals of rationality in the words of Max Planck, who took the first step in his 1900 analysis of blackbody radiation starting from a proclaimed ultra-violet catastrophe. 

To avoid catastrophe Planck introduced a concept of smallest quantum of energy $h\nu$ connected to light of frequency $\nu$ and $h$ a small constant, which was picked up by the young Einstein in 1905 in a "heuristic" explanation of the photoelectric effect returning to Newton's since long abandoned idea of light as a stream of light particles each carrying an energy $h\nu$. From these acts of desperation was then  StdQM born 20 years later as a Schrödinger equation in terms of a multi-d wave-function carrying probabilities of distributions of quanta of energy.   

So was modern physics as StdQM formed by modern physicists under the condition that blackbody radiation and the photoelectric effect cannot be explained within classical continuum physics.

If this condition would show to not be binding, then the premises for modern physics would change. RealQM offers an explanation of both blackbody radiation and the photoelectric effect which is based on a threshold condition on wave frequency $\nu$ as a condition on spatial resolution instead of any quanta of energy. RealQM thus offers a Unified Field Theory within classical continuum mechanics of matter+light over all scales, which was the unfinished dream of both Einstein and Schrödinger,   

PS. I checked with chatGPT what could have happened if blackbody radiation, photoelectric effect and atomic spectra had been resolved within classical continuum mechanics, as suggested by RealQM, and got this counterfactual answer:

• ✅ Yes: Up through ~1920, a clever deterministic continuum model could plausibly have “explained away” choseblackbody, photoelectric, and spectra. Physics might have developed as a wave-resonance continuum theory instead of quantum mechanics.
• ❌ But: Once Compton scattering and single-particle double-slit came in, the cracks would show. The particle-like momentum transfer and the self-interference of single quanta are incompatible with any local classical continuum.
• So your hunch is right: a classical deterministic continuum could have survived if physics stopped before Compton + double-slit. But with those experiments, and later Bell tests, the “classical-only” path would collapse.   

We see that modern physics was not really forced to follow the track chosen by Bohr-Born-Heisenberg under protests from Schrödinger...  

Schrödinger Equation Anniversary 1926-2026

In March 1926 the 39 year old Austrian physicist Erwin Schrödinger published an article entitled Quantisation as Eigenvalue Problem presenting a mathematical model of a Hydrogen atom with one electron in terms of classical continuum mechanics, which kick-started modern physics into the era of Quantum Mechanics, since it exactly captured the observed spectrum of Hydrogen.

The success was complete, and Schrödinger was very happy with his one-electron mathematical model as a wave equation in terms of a wave function representing electron charge density of clear physical nature like any density of classical continuum mechanics. 

But the happiness did not last long, since his one-electron model was quickly generalised to atoms with $N>1$ electrons in the hands of Bohr-Born-Heisenberg BBM in terms of a wave function $\Psi$ depending on $3N$ spatial coordinates, which could only be given a probabilistic meaning and so could not be accepted by Schrödinger with his deep conviction of physics as reality. The effect was that Schrödinger was quickly "cancelled" and had to spend the rest of his life as outsider without any say. The success was turned into its opposite.      

At a Dublin 1952 Colloquium Schrödinger restated his deep conviction carried for 26 lonely years that history took the wrong turn after March 1926 when his Schrödinger equation for Hydrogen was hijacked by Bohr-Born-Heisenberg to form the Copenhagen Interpretation as Standard Quantum Mechanics StdQM, which has filled text books, students and physicists minds for 100 years and still does:    

• Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today,
• I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.
• It has been worked out in great detail to form a scheme of admirable logical consistency that has been inculcated ever since to every young student of theoretical physics.
• The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it. 
• It is, as I said, the probability view of quantum mechanics. You know how it pervades the whole system. It is always implied in everything a quantum theorist tells you. Nearly every result he pronounces is about the probability of this or that or that ... happening-with usually a great many alternatives. The idea that they be not alternatives but all really happen simultaneously seems lunatic to him, just impossible. 
• He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. 
• It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way-namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation, which need, of course, not be a scientific observation.
• Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it. 
• And I wonder that he is not afraid, when he puts a ten pound-note {his wrist-watch} into his drawer in the evening, he might  find it dissolved in the morning, because he has not kept watching it.

Real Quantum Mechanics RealQM is an alternative to StdQM formed in the spirit of Schrödinger. It is quite possible that RealQM would have made Schrödinger happy again. If you are unhappy with StdQM, try RealQM! To get started check out recent posts e g the previous on Unified Field Theory with RealQM.

Unified Field Theory: Newton + Maxwell + RealQM

Schrödinger created Quantum Mechanics by formulating in 1926 a mathematical model within classical continuum mechanics in terms of a wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ satisfying a wave equation named Schrödinger's Equation SE: 

• $i\frac{\partial\psi}{\partial t}+H\psi =0$     (SE)

with 

• $H=-\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$ a Hamiltonian differential operator.

The eigenvalues of SE showed to exactly fit with the observed spectrum of a Hydrogen atom and so was the answer to a search begun by Bohr 15 years before. The success was complete: SE revealed the secret of the Hydrogen atom as an eigenvalue problem for a Hamiltonian with time-independent normalised real-valued eigenfunctions $\Psi (x)$ with energies as sum of kinetic and potential energies appearing as eigenvalues:

• $E = E_{kin}+E_{pot}=\frac{1}{2}\int\vert\nabla\Psi\vert^2dx-\int\frac{\Psi^2(x)}{\vert x\vert}dx.$ 

The ground state of a Hydrogen atom took the physical form of a charge density $\Psi^2(x)$ with minimal energy appearing as a compromise of negative $E_{pot}$ by concentration near $x=0$ balanced by a positive $E_{kin}=-\frac{1}{2}E_{pot}$ appearing as a form of "compression energy".

SE took the form of classical continuum mechanics with a clear physical interpretation as charge density and so represented a complete success of classical mathematical physics suddenly expanding its excellent service from macroscopics into atomic microscopics. 

SE combines perfectly with Newtonian gravitation giving $\Psi^2(x)$ a double role as both charge density and mass density, as well as with Maxwell's electro-magnetics. The resulting Newton-Maxwell Schrödinger NMS model was a Unified-Field-Theory covering all of Hydrogen physics from galactic to atomic scales. A tremendous success of mathematical modelling of real physics! Since Hydrogen accounts for 74% of the mass of the Universe NMS captured nearly everything.

But 25% is Helium and 1% all the other atoms, and so SE had to be extended to atoms with more than one electron like Helium with two electrons to qualify as UFT. But how?

A quick formal resolution lay on the table: Give each new electron a whole set of 3d coordinates and trivially extend (SE) to any atom with a stroke of a pen. That gave a wave function depending on $3N$ space coordinates for an atom $N$ electrons. Easy to do but without clear physical meaning. 

Schrödinger refused to take this step, but Bohr-Born-Heisenberg jumped on the band wagon of Standard Quantum Mechanics StdQM based on a multi-d Schrödinger equation forming the foundation of modern physics under heavy protests from Schrödinger because it replaced causality and physicality by non-physical probabilities of observer measurement outcomes. 

In short StdQM is viewed to be the result of a process of quantisation preventing unification with the classical continuum physics of Newton and Maxwell, which has grown out into the deep crisis of modern physics of today.

Since Maxwell and Newton represent perfect theories, without any need of quantification, the natural idea to form a UFT is to search for a form of QM without quantification. But this has been prevented for 100 years by the very strong domination of the Copenhagen Interpretation of Bohr-Born-Heisenberg. Efforts have been made of  "dequantisation" of StdQM bringing it back to classic continuum physics (e g Bohmian mechanics), but without success because quantification cannot be reversed. 

RealQM offers a generalisation of SE for Hydrogen to atoms with more than one electrons, which stays within the realm of classical continuum physics, and so combines perfectly with Newton and Maxwell into a UFT.  

 

Radiative Equilibrium Without Quanta: Normality

Consider a Hydrogen atom described by Schrödinger's Equation SE in radiative equilibrium with light of a certain frequency $\nu$ described by Maxwell's equations as an  electromagnetic wave. This means that there is a gap $\Delta E$ in the distribution of eigenvalues $E$ or spectrum such that $\Delta E =h\nu$ with $h$ a scaling factor, in classical literature named Plank's constant. 

The SE for Hydrogen is a partial differential equation of classical continuum form in terms of a wave function which changes continuously in space and time during the process of establishing and maintaining radiation at the resonance frequency $\nu$. The energy gap $\Delta E$ scales with the frequency $\nu$ over  the spectrum. 

What is discrete is the spectrum, just as in classical continuum mechanics, while wave functions are continuous and do not take any discrete "jumps" in state/energy.  

Conclusion: The Schrödinger's Equation SE for a Hydrogen atom takes the form of classical continuum mechanics. QM for a Hydrogen atom is classical continuum physics. No need for quantisation. The fact that the spectrum is discrete is not evidence that any non-classical process of quantisation is really needed. See also this post.

chatGPT: Maxwell + Schrödinger looks good:

• Treat the atom quantum mechanically (Schrödinger equation).

• Treat the radiation as a classical wave (Maxwell).

• That explains a lot: absorption spectra, stimulated emission, radiative equilibrium, Rabi oscillations.

• Everything looks continuous.

This model works surprisingly well in many normal conditions.

end chatGPT

But a modern theoretical physicist is not happy with normality of classical continuum physics as description of the basic problem of atom physics of a radiating atom, because it is not modern new physics. And so the modern physicist goes on to confront the radiating atom as classical continuum physics with some extreme circumstances such as very very weak forcing so weak that the continuity breaks down. Like running your car engine with only a very weak slow irregular ignition making the engine start to malfunction. This is called appeal to extremes often used in debate.

By focussing on some extreme case, the classical model covering the normal case can be downplayed as "wrong" even if it works fine, to prepare the way for some new bold modern theory, which is more "fundamentally correct". In this way all the victories of the classic theory for all normal cases can be cashed in for the new theory to which can then be added anything extreme even if vague. 

This is what is done when General Relativity replaces Newton's theory of gravitation as being more "fundamentally correct". Or when QFT replaces QM which replaces Schrödinger+Maxwell. More and more extreme to downplay the normal.

So can unsuccessful explanation of something normal within classical continuum mechanics, be covered up by focussing the interest onto something more fundamental and extreme, and the possibility of a classical explanation can be missed, as that of RealQM.   

The Spell of Quantisation = Crisis of Modern Physics

The fundamental difference between modern physics in the form of Quantum Mechanics QM and classical physics in the form of Continuum Mechanics, is something named 

• Quantisation. 

After a long discussion with chatGPT the following conclusion as "Honest Summary" is reached:

• Quantisation means: interactions are granular, in units of Planck's constant $h$.
• It is detected physically through indivisible events (photoelectrons, Compton recoils, detector clicks).
• It is explained mathematically by replacing classical observables with operators whose spectra are discrete.
• But the mechanical reason why nature enforces this is not known. 
• It is a foundational mystery.

On the way we have learned that what Quantisation is not:

• Not simply probabilistic interpretation of wave function. 
• Not simply discrete spectrum of a continuous vibrating string/atom.
• Not simply discreteness of electron unit charge.
• Not discrete "light particles/photons".
• Not discrete "lumps of energy".  
• Not really QM but rather Quantum Field Theory for continuous fields with discrete excitations. 

But not really anything concrete beyond formalism mystery of what Quantisation is. 

The trouble with Quantisation is that it forces a split between classical continuum physics and modern quantised physics which prevents a unification of macroscopic physics of gravitation with microscopic physics of atoms including electromagnetics. 

Without knowing what Quantisation is, it is very difficult to check if the split with continuum physics is really necessary. 

The fact that modern physics has not been able to form a Unified Field Theory UFT represents a monumental failure, which is now causing a deep credibility crisis of theoretical physics. 

Modern physics is thus confronted with the following spell:

1. Quantisation is necessary.
2. Quantisation prevents a UFT.
3. Lack of UFT is the root cause to the present deep crisis of theoretical physics.
4. Quantisation is a mystery.

But based on 4. it is natural to ask if 1. is true? 

To question 1. requires a QM without Quantisation and there is a candidate for such a thing in the form of Real Quantum Mechanics RealQM which has the form of classical continuum mechanics and so allows unification. 

With RealQM the spell of Quantisation evaporates and a UFT appears as a real possibility to explore. Want to try it? 

Recall that the 1. is the leading idea today of professional physicists: The only way forward towards unification is quantising gravitation, and the only hope went to String Theory emerging 50 years ago, but this hope is now quickly eroding. No hope any more for quantising gravity. 

The only way forward is to dequantise QM. This is what RealQM offers. 

Quantum Mechanics Without Quantisation

Schrödinger's Equation SE for the Hydrogen atom with one electron has the form of a classical continuum mechanical wave equation in a complex-valued wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ with $\vert\psi (x,t)\vert^2$ assigned the clear physical meaning of electron charge density at $(x,t)$ with total charge of one unit. The model captures the observed spectrum of Hydrogen as a discrete set of eigenvalues of normalised eigenfunctions in fully classical continuum mechanical form. 

Yet this model has been taken as starting point for a fundamental reformation of classical physics into a fundamentally new form of physics named quantum mechanics resulting from a process of quantisation. In the case of the Hydrogen atom this radical step reduces to a reinterpretation of $\vert\psi (x,t)\vert^2$ as a probability density thus replacing charge density (with physical meaning) with probability (without physical meaning). In this case the reformation makes no sense: The Emperor's New Clothes. Smallest quantum of energy has no physical meaning. 

The reason for the reformation appeared along with the generalisation of SE to atoms with more than one electron, which was the problem facing Schrödinger in 1926 after formulating SE for the Hydrogen atom with one electron, which propelled him to fame. But it was not evident how to proceed and so Schrödinger gave in to a purely formal generalisation introducing a new set of 3d spatial variables for each new electron forming a multi-d SE with only probabilistic interpretation possible and as such aggressively promoted by Bohr-Born-Heisenberg overpowering Schrödinger's request for real physics as ontology instead of unphysical probability as epistemology.

So was the modern physics of quantum mechanics born from a formal process of quantisation, which boiled down to replacing classical deterministic continuum physics by probabilistic physics without determinism and physical meaning. Schrödinger deeply regretted ever to be involved in this project forming 20th century physics. 

Could history have taken a different route by a different generalisation staying within classical continuum physics if Schrödinger had just resisted the onslaught from Bohr-Born-Heisenberg at bit longer? Yes, this would have been possible if only Schrödinger had tried the idea of Real  Quantum Mechanics RealQM of forming a SE in terms of non-overlapping charge densities with direct physical meaning and without any need of reformation by quantisation into probabilities. 

RealQM offers a model of atomic physics in the form of classical continuum physics without any need of quantisation and probabilities. RealQM combines seamlessly with classical electro-magnetics and Newtonian mechanics and so opens to the formation of a Unified Field Theory UFT, which both Schrödinger and Einstein struggled to find throughout the later halfs of their scientific lives, but couldn't do.....Schrödinger died in Vienna in 1961 73 years old... 

Schrödinger in his Nobel Lecture 1933 showing his resistance to Bohr-Born-Heisenberg:

• We cannot, however, manage to make do with such old, familiar, and seemingly indispensible terms as "real" or "only possible"; we are never in a position to say what really is or what really happens, but we can only say what will be observed in any concrete individual case. 
• Will we have to be permanently satisfied with this. . . ? On principle, yes. On principle, there is nothing new in the postulate that in the end exact science should aim at nothing more than the description of what can really be observed. 
• The question is only whether from now on we shall have to refrain from tying description to a clear hypothesis about the real nature of the world. 
• There are many who wish to pronounce such abdication even today. But I believe that this means making things a little too easy for oneself.

ChatGPT about Schrödinger's struggle find a UFT:

• After inventing wave mechanics, Schrödinger spent decades searching for a unified continuum field theory of matter and forces, resisting the idea that nature is fundamentally quantised — but his attempts never succeeded against the empirical dominance of quantum field theory.

• Goal: Matter = continuous wave fields, not particles.

• Method:

  • Original 1926 wave mechanics: electrons as standing waves.

  • Later: attempts to merge wave mechanics with Einstein’s relativity → affine field theory, complex scalar fields.

• Belief: Quantisation is not fundamental, but an artifact of wave modes and stability conditions.

• Outcome: His “unified field theory” never matched experiments; the community rejected it once QED and QFT succeeded.

• Spirit: Continuity is real, discreteness is emergent.

  
  

The Deep Secret of $E=h\nu$ Uncovered = 0

The value of Planck's constant $h$ is supposed to carry a deep secret of the atomic physics captured in the Schrödinger Equation SE of Quantum Mechanics QM as the foundation of modern physics. A deep secret of a microscopic world which is fundamentally different from the macroscopic world we can fathom by direct experience. A strange world of the modern physics emerging in the beginning of the 20th century, which "nobody understands" including the physical meaning of Planck's constant $h$. 

In the new 2019 SI standard of units, the value of $h$ is specified to be exactly $h=6.62607015\times 10^{−34}$ Joule-seconds, which is a very small number viewed to hide a deep secret, while appearing as an arbitrary unit conversion factor. 

Let us seek to untangle the secret in detail. We recall the message of modern physics of the existence of a smallest quantum of energy $h\nu$ associated to a wave of frequency of $\nu$ showing that the microscopic world is discrete and not continuous like the macroscopic world so well described by continuum mechanics. More precisely, light as a wave phenomenon is viewed to consist of a stream of light particles named photons each one carrying exactly the energy $h\nu$. Mind boggling, suggesting some deep secret.

Let us now trace the connection to SE for the Hydrogen atom taking the form: 

• $ih\frac{\partial\psi}{\partial t} + H\psi =0$                (SE)

where $\psi (x.t)$ is a complex-valued wave function depending on a 3d spatial coordinate $x$ and a time variable $t$ and $H$ is a (Hermitian) operator acting on $\psi$ with a discrete spectrum of real eigenvalues $E$ representing energies of normalised eigenfunctions $\Psi (x)$ satisfying $H\Psi =E\Psi$, which give wave solutions to (SE) of the form 

• $\psi (x,t)=\exp(i\frac{E}{h}t)\Psi (x)=\exp(i\nu t)\Psi (x)$ with
• $\nu =\frac{E}{h}$ or $E=h\nu$.  

We thus see a direct connection between the smallest quantum of energy $h\nu$ and energies $E=h\nu$ of eigenstates/functions of a Hydrogen atom, as a direct reflection of the form of (SE) including a first time derivative: Energy $E$ scales linearly with frequency $\nu$. 

The other way around, one can see (SE) as being formed by Schrödinger to include the connection $E=h\nu$ between energy $E$ and frequency $\nu$ (as a linear dispersion relation), because that fits with observed spectrum of the Hydrogen atom. Mathematical modeling to fit observation.   

More precisely, the spectrum of a Hydrogen atom comes out from differences of eigenvalues/energies $\Delta E$ translated to frequencies by $\Delta E =h\nu$. 

The basic heuristic idea of Einstein in 1905 was that  the energy of the electron of a Hydrogen atom can "jump" from one energy level to another by receiving/delivering exactly one photon of energy $\Delta E =h\nu$ in radiative equilibrium with light of frequency $\nu$: 

• Transition from one energy level to another with an energy jump $\Delta E$ of the electron of a Hydrogen atom involves receiving/delivering exactly the energy $\Delta E=h\nu$ of one photon of frequency $\nu =\frac{E}{h}$. 

This idea is supposed to convince us that the world of a Hydrogen atom is discrete operating with discrete chunks of energy $h\nu$ carried by discrete light particles/photons.

But this is an invented discreteness: SE is a continuum model of classical form in a wave function $\psi$ with $\vert\psi (x,t)\vert^2$ representing charge density, which has a discrete set of eigenvalues just like a vibrating string. The association of energy to frequency by $E=h\nu$ is simply a scaling of between energy and frequency with a scaling factor of $h$ with a value depending on choice of units.

From (SE) it follows that size of a Hydrogen atom scales with $h^2$ which connects to the discreteness of a Hydrogen atom with its only electron, which is described by the continuous model (SE) of classical continuum form. 

We thus find nothing fundamentally different from classical continuum mechanics point of view in the (SE) model of a Hydrogen atom in terms of a charge density. The association of an energy jump $\Delta E =h\nu $ to exactly one photon of frequency $\nu$ lacks real physical meaning and is just a convention which appeared as a heuristic idea in Einstein's mind in 1905. Planck's constant $h$ does not say that the microscopic world is discrete making it fundamentally different from a continuous macroscopic world. Planck's constant has a meaning as setting the physical scale of a Hydrogen atom, but not as a deep secret about the world. Of course atoms have spatial size just as specific macroscopic material objects with specific spatial extension. A Hydrogen atom is a like a continuous string of a violin of certain length and tension. No quantum.

In short, the quantum world of a Hydrogen atom can be understood in terms of classical continuum mechanics. 

The split appears when generalising (SE) to atoms with $N>1$ electrons following the route of Standard QM by Born-Bohr-Heisenberg into a linear wave equation in $3N$ spatial dimensions, with the wave function given a probabilistic unphysical meaning which makes StdQM "not understandable".

RealQM offers a fundamentally different generalisation without split away from classical continuum mechanics, which is understandable.  

Summary: 

1. Planck's constant $h$ serves as a formal conversion factor between energy $\Delta E$ and frequency $\nu$ with $\Delta E=h\nu$ in the setting of a radiating  Hydrogen atom. The size of a Hydrogen atom scales with $h^2$ which gives the specific value of Planck's constant $h$ a physical meaning, which is not some deep secreted of smallest quantum of energy. 
2. The generalisation to any atom by StdQM leaves classical continuum mechanics into a probabilistic quantum world "nobody can understand" where Planck's constant appears as a deep secret.
3. RealQM offers a generalisation staying within the form of classical continuum mechanics which "everybody can understand" where Planck's constant remains the simple conversion factor of 1. = No Secret = 0.
4. RealQM appears as "Quantum Mechanics without Quantum" which opens to unification with electromagnetics-Newtonian gravitation into a Unifies Field Theory as unfinished dream of Einstein. Let's get to work! 

Brief Quantum Story 1900 - 1905 - 1925 - 2025

The first form of the Schrödinger equation presented by Schrödinger in 1926  offered a mathematical model of the Hydrogen atom with one electron in the form of a linear wave equation of classical continuum mechanical form in terms of a (complex valued) wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ with $\vert\psi (x,t)\vert^2$ representing charge density at $(x,t)$ with total unit electron charge. The corresponding classical eigenvalue problem with discrete eigenvalues showed to fit exactly with the observed discrete spectrum of Hydrogen. 

The success was immense and Schrödinger rocketed to fame by giving birth to a new form physics of atoms to be named Quantum Mechanics QM, but it was not Schrödinger who coined the concept of quantum, and in fact he disliked it from the bottom of his heart:

• If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.

Recall from recent posts that that the quantum was the result of desperate actions by first Planck in 1905 introducing a quantum of energy $h\nu$ associated with radiation of frequency $\nu$ with $h$ a very small constant indicating that a quantum of energy is a very small quantity. Einstein followed in 1905 by suggesting that light of frequency $\nu$ could be thought of (heuristically only!) as a stream of light particles or photons each photon carrying exactly one quantum of energy $h\nu$. Vivid fantasy.

Then 20 years passed with the idea of the quantum of energy $h\nu$ kept as a form of easy fix to explain blackbody radiation and photoelectricity believed to be impossible within classical continuum physics. 

Schrödinger gave his revolutionary Hydrogen article the title "Quantisation as Eigenvalue Problem" thus connecting back to the a concept of "quantisation" suggested earlier by Bohr and de Broglie and coming out in Heisenberg's matrix mechanics, which he now reformulated as an eigenvalue problem of the form of classical continuum physics. Schrödinger's goal was to show that the new quantum mechanics of atoms in fact could take the form of classical continuum mechanics. Schrödinger never gave up that goal but could only reach it in the case of the Hydrogen atom with one electron, since already the Helium atom with two electrons appeared to require a new model outside classical continuum mechanics, and so Schrödinger left QM in 1928 disgusted, to let it be formed by Bohr-Heisenberg as a fundamentally new form of physics as QM, which has come to serve as the foundation of modern physics, without Schrödinger the founder of QM 

But back to Schrödinger's equation for the Hydrogen atom, which does not ask for any quantum of energy $h\nu$ carried by a photon. It is a classical continuum physics eigenvalue problem with discrete spectrum of eigenvalues $E_1<E_2<E_3,...$ representing energies of excited states staring from a ground state energy $E_1$. Differences of eigenvalues $E_n-E_m$ with $E_n>E_m$ match with frequencies $\nu$ in the observed spectrum of Hydrogen under scaling with a certain constant $h$. There is here only a superficial connection between a classical continuum physics eigenvalue problem and the new concept of quantum of energy scaling with frequency $\nu$.  Schrödinger managed to turn quantisation into a classical eigenvalue problem. 

Once the Hydrogen atom was secured within classical continuum physics without the real need of any quantum of energy $h\nu$, which he disliked so much, Schrödinger took on the Helium atom with two electrons. And this is where history took a turn with far-reaching consequences into our time. Instead of staying within classical continuum physics, Schrödinger and everyone else took the easy way out by generalising from one electron to many electrons by a purely formal procedure leaving out physics. For some reason, Schrödinger and everyone else missed the possibility demonstrated in Real Quantum Mechanics RealQM of staying within classical continuum physics without need for any quantum of energy. 

The result of taking the easy formal route when generalising Schrödinger's equation from one electron to many and so form StdQM as the textbook version of QM today, is that "nobody understands QM", simply because the easy formal route does not make sense from physical point of view. What does not make sense cannot be understood, and if something cannot be understood, it is because it does not make sense. 

What about giving RealQM a try, if you want to understand QM? RealQM offers an understanding of blackbody radiation and photoelectric effect with a frame of classical continuum physics!

Recall this statement by Lieb and Thirring from this post concerning the easy way out:

• An important historical point is to be noted here. It might have been thought that the correct generalization for N particles is to use N functions of one variable instead of one function of N variables. 
• Such a ‘wrong turn’ did not happen historically, which is, after all, remarkable.

What did not happen was RealQM and so when it now happens 100 years later it may be remarkable.

Photon Energy =$ h\nu$ as Deep Secret of Modern Physics?

In a classical wave equation the frequency in time $\nu$ scales with $\sqrt{E}$ with $E$ wave energy, or the other way around energy $E\sim \nu^2$. To see this recall that a classical wave appears as a real-valued solution $\phi (x,t)$ to the following classical wave equation (with $\phi_t$ the derivative with respect to $t$):

• $\phi_{tt}-\phi_{xx} =0$ for $0<x<\pi$ and $t>0$,                         (1)
• $\phi (0,t)=\phi(\pi ,t)$ for $t>0$,
• $\phi (x,0)$ and $\phi_{t}(x,0)$ given initial values.

A typical solution has the form 

• $\phi(x,t)=\cos(\nu t)\sin(\nu x)$ with $\nu =1,2,3,..$ as natural number, 
• with energy $E\equiv \int_0^\pi\vert\phi_{xx}\vert ^2dx\sim \nu^2$
• thus with frequency $\nu\sim \sqrt{E}$.  

On the other hand we know the convention of assigning the energy $E=h\nu$ to a photon in Standard Quantum Mechanics, thus as $E\sim \nu$, with $h$ a constant, which can be anything but is  prescribed to have a certain standard value in the SI Standard.  

So in classical wave mechanics $E\sim\nu^2$ and in quantum mechanics $E\sim\nu$, which to a student must be confusing, in particular since $E=h\nu$ is supposed to have a deep secret meaning. 

So why this difference? The reason is that the wave equation of quantum mechanics does not take the above form, but instead the following complex form with only one derivative in time:

• $i\phi_{t}-\phi_{xx}$ for $0<x<\pi$ and $t>0$,                         (2)
• $\phi (0,t)=\phi(\pi ,t)$ for $t>0$,
• $\phi (x,0)$ given initial value,

with typical solution 

• $\phi(x,t)=\exp(i\nu^2 t)\sin(\nu x)$ with $\nu =1,2,3,..$,  
• with energy $E\equiv \int_0^\pi\vert\phi_{xx}\vert ^2dx\sim \nu^2$,
• thus with frequency $\nu\sim E$.  

We understand that the complex form (2) can be reduced to real form:

• $\phi_{tt}-\phi_{xxxx}$,

to be compared with the classical $\phi_{tt}-\phi_{xx}$, which explains the switch from $E\sim \nu^2$ to $E\sim\nu$. 

We have learned that the connection $E=h\nu$ simply reflects the nature of the wave equation adopted and as such carries no deep secret per se and only represents an ad hoc division of global energy into little quanta which have no realisation in physics. 

If we connect an atom naturally described by (2) to light naturally described by (1), the we have to take the difference in chosen wave equations into account when connecting atomic energy and light energy recalling that incoming wave energy scales like $\nu^2$ resulting from $\nu$ incoming energy quanta of size $\nu$ per unit of time. 

The post points to basic aspects and does not seek to give a detailed account using 3d Maxwell equations for light and Schrödinger's eq for an atom. The idea is to decode the proclaimed deep secret of light particles/photons carrying energy quanta $h\nu$.

Notice that the macroscopic wave equation (1) describes waves which move rectilinearly in space, while (2) describes atomic waves which rather rotate on the spot while keeping charge density constant.  Schrödinger's equation thus connects to (2) in direct opposition to any concept of electrons moving around a nucleus.  

Classical Normal Physics vs Modern Extreme Physics

This is a reflection on the previous post opening to a "quantum mechanics without quantum" as a continuum world possible to describe by the fields of classical continuum physics. If indeed this is a real possibility, it might be worthwhile to pursue. Ok?

To learn about some physics there are two fundamentally different approaches: (i) start with the normal and (ii) start with the extreme. For example, to learn about the physics of sailing you may (i) start with normal conditions or (ii) start with the extremes of no wind or hurricane. What would be your advice?

With the opposites of normal and extreme, we can identify:

1. Classical Physics = reality of continuum we see as normal physics. Illusion of discreteness on all scales.  
2. Modern Physics = reality of small scale discrete/quantum we see only as extreme physics. Illusion of continuity on large scales. 

This is the split between continuum physics and quantum physics which has haunted the science of physics for 100 years into the present deep crisis, because 2 has been adopted to direct the efforts following the legacy of Bohr-Born-Heisenberg, which made 1 into fringe physics carried by Schrödinger-Einstein.

The big trouble with 2. is the break with 1. preventing unified physics on all scales leading to a crisis.

The fundamental idea of 2. is "quantisation" as a vague procedure to split things into little pieces not in physical meaning, but into some form of book-keeping units of "quanta". This is the idea of "quantisation of light", which is a continuous electromagnetic wave phenomenon very well described by Maxwell's wave equation over a 3d spatial continuum, by insisting that a wave of frequency $\nu$ can be chopped up in small units of energy $h\nu$ named photons where $h$ is a very small constant. This is a form of book-keeping without physics, since the physics of a photon has never been made clear.  

In any case, to support 2. experiments have been set up to prove the existence of photons simply by identifying a single photon experimentally. Since $h\nu$ is very small that requires an extremely sensitive detector which gives exactly "one click per photon". The assumption is then that since a click is discrete, what makes the click appear must also have been discrete and that is the photon! So can the existence of the photons as real discrete physics be proved by a click on a screen. The same with the Higgs boson proved to exist by a blip on a screen in 2015 in an extreme LHC experiment! LIGO also extremely extreme!

 

Thus major efforts have been spent on supporting 2. as the essence of modern physics, while 1. has been kept short to be pursued in philosophical circles without experimental devices capable of detecting normality.

With the deepening crisis resulting from 2. it may now be possible to open for a renewed focus on 1. as a continuum world of normality of great complexity. That is the objective of RealQM. 

My question to chatGPT: Which experiment forced quantisation (upon resisting physicists)?

Answer:

• Planck (1900): introduced quantisation as a desperate fix.

• Einstein (1905): pushed photons as real, but not widely accepted.

• Bohr (1913): extended discreteness to atoms.

• Compton (1923): gave overwhelming evidence photons are real quanta. → This was the true turning point.

By the mid-1920s, physicists gave up resisting. Quantum mechanics (Schrödinger 1926, Heisenberg 1925) became the new framework.

My comment: All of the above phenomena can be explained as continuum physics as discussed in previous posts and shown in Computational Blackbody Radiation. It appears that physicists have been more than willing to be forced into extreme positions to fill the need of sensation headline physics of modernity. It may also seem heroic to stick to an extreme principle under heavy skepticism from normality: We simply "have to give up" the rationality of the normal because physics is "weird" and something that "nobody can understand". But maybe we do not have to do that?

Maybe the time for Big Physics as extreme physics is coming to an end, in the deepening crisis, where the  next even bigger Large Hadron Collider for extreme physics will not be built, because there is nothing more of the extreme to be detected because physics is exhausted on extremely small scales, and that the real complex physics of interest takes place on scales larger than the smallest, which can be detected by affordable apparatus.

Here is a problem for normal physics still open after 100 years: 

• Explain the Periodic Table by QM,  in particular the periodicity 2,8,8,18,18,32,32,... 

Theoretical physicist: This was done long ago, in principle, but details were left to chemists. 

Theoretical chemist: I have been trying for a long time without much success. A basic problem is that I do not understand QM well enough and I get no help from a theoretical physicist who says that an explanation was given long ago, in principle....